Related papers: Quantum mechanics in a cut Fock space
A formulation of quaternionic quantum mechanics ($\mathbb{H}$QM) is presented in terms of a real Hilbert space. Using a physically motivated scalar product, we prove the spectral theorem and obtain a novel quaternionic Fourier series. After…
We outline selected trends and results in theoretical modeling of quantum systems in support of the developing research field of quantum information processing. The resulting modeling tools have been applied to semiconductor materials and…
Quantum advantage is well-established in centralized computing, where quantum algorithms can solve certain problems exponentially faster than classical ones. In the distributed setting, significant progress has been made in…
A new quantum-stochastic differential calculus is derived for representing continuous quantum measurement of the position operator. Closed nonlinear quantum-stochastic differential equation is given for the quantum state of the observed…
We review canonical experiments on systems that have pushed the boundary between the quantum and classical worlds towards much larger scales, and discuss their unique features that enable quantum coherence to survive. Because the types of…
Interest in problems of statistical inference connected to measurements of quantum systems has recently increased substantially, in step with dramatic new developments in experimental techniques for studying small quantum systems.…
This paper provides an examination of how are prediction of standard quantum mechanic (QM) affected by introducing a noncommutative (NC) structure into the configuration space of the considered system (electron in the Coulomb potential in…
The completeness of quantum state space, is usually expressed as \sum_{m=0}^{\infty}|m><m|=1, where {|m>} is selected set of quantum states (basis). Density matrix |m><m| describes a pure quantum state. In this paper, by virtue of the…
Quantum computing promises the possibility of studying the real-time dynamics of nonperturbative quantum field theories while avoiding the sign problem that obstructs conventional lattice approaches. Current and near-future quantum devices…
Continuously measured quantum systems are characterized by an output current, in the form of a stochastic and correlated time series which conveys crucial information about the underlying quantum system. The many tools used to describe…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
We analyze the passage to a continuum limit of the mode spectrum of primordial perturbations around flat cosmological spacetimes in Quantum Cosmology, showing that this limit can be reached even if one starts by considering a finite…
The construction of a consistent theory for structuring and representing how concepts combine and interact is one of the main challenges for the scholars involved in cognitive studies. All traditional approaches are still facing serious…
The functional method, introduced to deal with systems endowed with a continuous spectrum, is used to study the problem of decoherence and correlations in a simple cosmological model.
We describe quantization schemes for scalar field cosmology in the metric variables with fundamental discreteness imposed with a lattice. The variables chosen for quantization determine the lattice, and each lattice produces distinct…
Inhomogeneous quantum cosmology is modeled as a dynamical system of discrete patches, whose interacting many-body equations can be mapped to a non-linear minisuperspace equation by methods analogous to Bose-Einstein condensation.…
A system of quantum reasoning for a closed system is developed by treating non-relativistic quantum mechanics as a stochastic theory. The sample space corresponds to a decomposition, as a sum of orthogonal projectors, of the identity…
We report the close form expressions of the photon number statistics for a generalized coherent state and a generalized photon-added coherent state, which are shown to be crucial for proposing a variety of quantum scissor operations. The…
I propose a version of quantum mechanics featuring a discrete and finite number of states that is plausibly a model of the real world. The model is based on standard unitary quantum theory of a closed system with a finite-dimensional…
As experiments continue to push the quantum-classical boundary using increasingly complex dynamical systems, the interpretation of experimental data becomes more and more challenging: when the observations are noisy, indirect, and limited,…